Chiral self-assembly of cellulose nanocrystals is driven by crystallite bundles

The transfer of chirality across length-scales is an intriguing and universal natural phenomenon. However, connecting the properties of individual building blocks to the emergent features of their resulting large-scale structure remains a challenge. In this work, we investigate the origins of mesophase chirality in cellulose nanocrystal suspensions, whose self-assembly into chiral photonic films has attracted significant interest. By correlating the ensemble behaviour in suspensions and films with a quantitative morphological analysis of the individual nanoparticles, we reveal an inverse relationship between the cholesteric pitch and the abundance of laterally-bound composite particles. These ‘bundles’ thus act as colloidal chiral dopants, analogous to those used in molecular liquid crystals, providing the missing link in the hierarchical transfer of chirality from the molecular to the colloidal scale.


Calibration of sonication dose by calorimetry
The impact of ultrasonication of CNC suspensions depends on the properties of the suspension (volume and CNC concentration), the settings on the tip sonicator (tip amplitude) and the duration of the treatment (Supplementary Figure 1A). Although sonication is frequently applied to CNC suspensions and the equipment settings are often provided in the literature, it can be difficult to make quantitative comparisons between results. To explore the consistency of sonication across different experimental conditions, the hydrodynamic diameter of CNC particles after various sonication treatments was measured using DLS (Supplementary Methods, section 12.1). The different treatment conditions are summarised in Supplementary Figure 1B). To quantify the impact of sonication in a device-independent manner, it is necessary to express the sonication dose as the total energy delivered to the system by the sonicator tip. As sonication increases the temperature of the suspension, the energy delivered to the suspension can be estimated by calorimetry. Calorimetry was performed using a custom-made bomb calorimeter, consisting of a cylindrical chamber of expanded polystyrene foam surrounding a centrifuge tube to thermally insulate the sample. The temperature was measured using a thermocouple (Thorlabs TSP01) within the chamber. A magnetic stirrer bar was used to maintain mixing of the suspension.
First, the power delivered to a sample of 40 g deionised water was determined for a range of values for the amplitude of the sonicator tip (expressed as a percentage of the maximum amplitude, % ), as shown in Supplementary Figure 1C. Using this calibration curve for (% ), the sonication energy delivered to the sample is given by where is the total duration of the sonication treatment (considering only the duration of the ON portion of the ON:OFF sonication cycles). This expression assumes that the CNC suspensions have the same specific heat capacity as water, which is a valid assumption at low CNC concentration. The decrease in hydrodynamic diameter (DLS z-average size) with sonication is shown in Supplementary Figure 1D-F, where the sonication dose is expressed in terms of sonication duration (Supplementary Figure 1D), energy per CNC dry mass ( = / CNC , Supplementary Figure 1E) and energy per suspension volume ( = / , Supplementary Figure 1F).
It is clear from Supplementary Figure 1D-F that the hydrodynamic diameter results are only consistent across all experimental conditions when the sonication dose is expressed using . Note that energy per CNC dry mass , a dose unit often used in the CNC literature, gives consistent results when comparing conditions at fixed CNC concentration, but not when comparing doses at different concentrations (Supplementary Figure 1E).

Pitch measurement by SEM on CNC film cross-sections
The pitch of CNC photonic films can be directly observed from the film cross-section in SEM images (Supplementary Methods, section 12.4). The helicoidal structure of CNC photonic films results in a periodic texture in SEM cross-sections, as shown for selected samples in Supplementary Figure 2. The pitch is determined from the vertical distance for one full rotation of the structure (corresponding to two repeats of the fingerprint pattern). Cross-sectional SEM images for = 0 J mL −1 and >2×10 3 J mL −1 appeared isotropic with no helicoidal texture.
Supplementary Figure 2: Examples of SEM cross-sections for CNC photonic films. Dose indicated by the value on each image. Scale bar is 1 µm.

Pitch measurement by optical spectroscopy on CNC photonic films
The left-handed helicoidal configuration of birefringent CNCs in a solid film results in selective reflection of left-circular polarised (LCP) light in a wavelength range determined by the cholesteric pitch . The peak reflection wavelength at normal incidence is given by where CNC is the average refractive index of the CNC film, which we assumed to be 1.555 based on previous reports (1).
Supplementary Figure 3: (A) Left-circular polarised (LCP) reflectance spectra of CNC photonic films. (B) Comparison of peak LCP reflectance wavelength from polarised optical microscopy POM and the predicted peak reflection wavelength based on SEM pitch values SEM = CNC SEM , assuming CNC = 1.555. The error bars for POM indicate the peak full width at half maximum, while the error bars for SEM indicate the standard deviation of the pitch measurements.
Left-circular polarised reflection spectra were obtained at a range of sonication doses (Supplementary Methods, section 12.3). The peak reflection wavelength increases with sonication dose, as shown in Supplementary Figure 3. The apparent peak for the never-sonicated sample ( = 0 J mL −1 ) could indicate the presence of some chiral nematic domains within the structure, although no ordering was visible in SEM images of the film cross-section (Supplementary Figure 2). This small peak could also be attributed to scattering in the disordered structure, or partial absorption by the reference silver mirror in this wavelength range. The peak reflection wavelength at high doses ( >2000 J mL −1 ) was too far into the infrared to be detected using this setup. There is reasonably good agreement between the peak LCP reflectance wavelength obtained by spectroscopy and the pitches measured by SEM (Supplementary Figure 2). Determination of CNC pitch by SEM tends to over-estimate the true value as the pitch of tilted chiral nematic domains appears larger when viewed from the plane of film breakage. The decrease in pH with sonication indicates that H + ions are released, and the associated contribution to the conductivity increase can be estimated from the pH shift. Explicitly, denoting the conductivity and pH of the never-sonicated suspension as 0 and pH 0 respectively, the expected conductivity contribution from H + ions is where Λ + (≈ 0.035 m 2 S mol −1 ) is the molar ionic conductivity of H + in aqueous solution, using the value at infinite dilution as an approximation (2). The estimated H + contribution compared to the experimental conductivity change is shown in Supplementary Figure 4. These results indicate that the release of H + ions is the dominant source of conductivity change. It is likely that the released H + ions originate from the acid hydrolysis used to produce the CNCs. It has been proposed that these released ions increase the effective particle volume and thereby cause a red-shift in the chiral nematic pitch by preventing short-range chiral interactions between CNCs (3). However, this argument seems to contradict the expected behaviour of charged colloids, where increasing ionic strength is usually found to reduce the thickness of the electric double layer (4). Furthermore, numerous studies have shown that increasing the ionic strength of liquid crystalline CNC suspensions results in a smaller pitch, leading to a blue-shifted colour in the photonic film (5). In this work, the suspensions were therefore extensively dialysed (> 1 week) after sonication, all in the same bath of deionised water, to rule out the influence of released ions. After dialysis, an apparent difference in conductivity was measured between samples and could not simply be attributed to variation in CNC concentration after dialysis (Supplementary Table 2 The simplest explanation of the higher conductivity values for sonicated suspensions after dialysis in Supplementary table 2 is that these suspensions contain more ions due to incomplete dialysis. Highly sonicated suspensions were also found to have lower pH values (data not shown), but pH values on low ionic strength suspensions are prone to error due to the diffusion of ions from the pH probe into the suspension. To more accurately quantify the suspension pH, we followed a recently reported procedure by preparing samples at fixed CNC concentration (1.50 wt%) with an excess of K + ions (50 mM KCl) to dislodge the H + ions from the CNC surface (6). Under these conditions, all five CNC suspensions were found to have the same pH value within experimental uncertainty (2.56±0.03), demonstrating that the overall number of H + counterions per CNC mass was identical. This result is in agreement with surface charge values determined by conductometric titration (section 4.2).
These results suggest that the apparently higher conductivity and lower pH for sonicated suspensions after dialysis are not due to incomplete dialysis, but can instead be attributed to increased counterion mobility after sonication. Tight binding of counterions to the CNC surface greatly reduces their effective mobility, and therefore their contribution to conductivity and pH measurements of dialysed CNC suspensions. This binding is weakened by sonication as the total CNC surface area increases (Supplementary Figure 10C), leading to higher conductivity values.

Surface charge and colloidal stability
The surface charge on CNCs influences their colloidal stability and self-assembly by modifying the electrostatic interactions between particles (7). The effect of sonication on the CNC surface charge was therefore investigated as a possible source of the observed variation in the chiral nematic pitch.
The CNC surface charge (expressed as moles of counterions per kilogram of CNC dry mass) was determined by conductometric titration (Supplementary Methods, section 12.5) after dialysis. As shown in Supplementary Table 3 the surface charge per CNC dry mass did not vary with sonication dose within the uncertainty of the fitting of the titration curve. The surface charge for these samples (≈ 153 mmol kg −1 ) corresponds to a CNC sulphur content of 0.49% (w/w), or a degree of substitution of 2.5% on glucose monomers.
Although the CNC specific surface charge (i.e. surface charge per mass) is readily accessible by experiment, a more relevant physical properties is charge per surface area , also known as the areal surface charge density, which is given by = /SSA, where SSA is specific surface charge (surface area per CNC mass). The SSA for a CNC particle of surface area Σ and volume is given by SSA = Σ/( CNC ), where CNC is the CNC mass density and assumed to be 1600 kg m −3 . For a distribution of particles, the mean surface charge density can be estimated by assuming the specific surface charge is identical for all particles, i.e.
as opposed to assuming the charge per surface area is identical (which would give ⟨ ⟩ ′ = /⟨SSA⟩). The CNC surface charge density value is therefore highly dependent on the method used to estimate SSA.
Estimates of the CNC charge per surface area obtained by three possible methods are shown in Supplementary Figure 5. The "TEM outline" estimate is obtained by calculating the average SSA using the SSA of each particle based on the surface area and volume estimates used elsewhere in this work (see section 7 and Supplementary Figure 10C). The "box" estimate is obtained in a similar way, but assumes that the CNCs are cuboidal, with length, width and thickness given by their box length , box width and mean thickness ⟨ ⟩ respectively (see section 7 for definitions of these properties). The box estimate consistently produces a higher value for ⟨ ⟩, due to higher estimates of the particle volume. Alternatively, as shown in previous works (e.g. (7)), the CNC surface charge density can be estimated by assuming the CNCs are identical cylinders with length and diameter given by the box length and thickness. Using this "mean cylinder" approach, substantially lower estimates for ⟨ ⟩ were obtained. These results illustrate the considerable uncertainty in estimating the surface charge density of CNCs. Nevertheless, all estimates predict a decrease in ⟨ ⟩ with sonication dose Estimates are based on true particle shape (circles), box properties (squares) or by assuming all CNCs are cylinders with identical length and diameter (pentagons). Estimation methods are described further in the text.
The decrease in CNC surface charge density shown in Supplementary Figure 5 may be expected to indicate a decrease in colloidal stability. However, a complementary measurement of the mean electrophoretic mobility of the particles was performed by measuring the zeta potential (Supplementary Methods, section 12.6), which showed no clear trend with sonication dose within the uncertainty of the measurements. This result suggests that the expected decrease in charge per surface area does not make the CNCs colloidally unstable, at least under the conditions of the zeta potential measurement (ionic strength ≈ 1 mM). However, the decrease in ⟨ ⟩ with sonication may explain the earlier onset of kinetic arrest at higher doses.
Sonication dose (J/mL) Specific surface charge (mmol/kg) Zeta potential (mV) 0 154.  In a log-log plot of turbidity versus wavelength (Supplementary Figure 6b), it is clear that alongside an overall decrease in turbidity at all wavelengths, sonication changes the shape of the turbidity spectrum, with a −3 wavelength dependence at low sonication dose transforming into a −4 dependence at high dose. This behaviour can be understood in terms of the morphological changes induced by sonication, and can be used to estimate the mean CNC particle cross-section (8).
For a turbid suspension of scattering dielectric particles in the limit of infinite dilution, light transmission obeys a Beer-Lambert-type decay with optical path length : For a suspension of identical particles , the turbidity is given by = / , where is the decay constant in Equation (4) above and is the particle concentration expressed as the number of particles per volume. If the particles are small compared to the wavelength ( −1/3 < ) and have mild refractive index contrast with the solvent medium (( − 0 )/ 0 ≪ 1), the turbidity can be approximated using the Rayleigh-Gans-Debye model: where is a geometric factor that depends only on the particle shape. The turbidity of CNC suspensions can be understood by comparing two ideal shapes: isotropic spheres and long slender rods. For spherical particles, ℎ = 1 and the turbidity is which is the conventional expression for Rayleigh scattering with −4 wavelength dependence.
For a slender rod with an extended length ≫ but sub-wavelength cross-section, the geometric factor is (9; 10) and the turbidity is therefore which has a −3 wavelength dependence. At low sonication dose, CNC particles behave like slender rods and therefore exhibit a −3 wavelength dependence. As sonication breaks apart the CNCs, reducing the particle volume and aspect ratio, their morphology becomes less elongated and a −4 wavelength dependence emerges (as seen in Supplementary Figure 6B). The turbidity equations given by eq. (5) are difficult to apply directly to CNC suspensions because the number density of CNCs ( ) cannot be directly measured, and there is considerable polydispersity in CNC size and shape. Therefore, we consider CNC suspensions as a population of different particle species , each with different particle volumes but identical refractive indices = 1 , suspended in a medium of index 0 . In this case, the turbidity decay constant in eq. (4) generalises to where ∑ indicates summation over all particle species. Experimentally, the most accessible concentration metric is the overall particle volume fraction, given by We therefore define the turbidity per volume fraction ′ = / , or explicitly For a distribution of slender rods (with given by Equation (7) for all particle species), we find that ′ = 66 3 where ⟨ ⟩ is the volume-weighted mean of the particle cross-section: Equation (12) can therefore be used to estimate the particle cross-section from the experimental transmission spectra (Supplementary Figure 6C), a technique that has previously been reported for CNC suspensions (8). Only the long-wavelength data ( > 400 nm) were used, as the assumptions used to derive Equation (12) are only valid in the long-wavelength limit.
The mean cross-section ⟨ ⟩ decreases with sonication dose (Supplementary Figure 6c) and approaches a limiting value of ≈ 70 nm 2 at high sonication dose.

Evidence of bundles from cryoTEM imaging
The preparation of CNC samples for conventional TEM imaging involves drying a droplet of sample onto the TEM grid, which can cause aggregates to appear in TEM images that do not exist in the original suspension. These artefacts should not be confused with CNC bundles, which are native to CNC suspensions at all sonication doses, or with large clusters of bundles at low sonication doses (classified as aggregates in the article). To illustrate that bundles are a native feature of CNC suspensions, cryoTEM imaging was performed on selected CNC samples (Supplementary Methods, section 12.8). In cryoTEM imaging, the CNC suspension is frozen and never dried, thus eliminating any risk of artefact creation. Example images are shown in Supplementary Figure 7. It is evident from qualitative inspection of the images that these suspensions contain CNCs with a bundled morphology.

Property Symbol Equation Units
Aspect ratio, oriented bounding box / -Aspect ratio, area-equivalent (AE)

Symbol Equation Units
Thickness, particle mean ⟨ ⟩ nm Area, particle surface

Estimation of CNC thickness using atomic force microscopy (AFM)
Atomic force microscopy (AFM) provides data on the topography of a sample surface, and therefore offers complementary morphological information to transmission electron microscopy (TEM). For CNCs deposited on a flat substrate and imaged using AFM, the mean and maximum thickness of the particle can be accurately measured, as illustrated in Supplementary Figure 11A. The lateral size of particles, as expressed as the Feret length and width (Supplementary Figure 11B), can also be obtained. However, it should be noted that the topography of the particle is convolved by the effective diameter of the AFM tip (Supplementary Figure 11C), which limits the use of AFM data for more detailed morphological analysis.
Supplementary Figure 11: Morphological properties obtained from atomic force microscopy (AFM). (A) Individual particles (also known as "grains" in AFM terminology) are identified as the region where the baseline-corrected surface height ( , ) exceeds a critical threshold value th (red dotted line). Each particle is defined as the bounded region that satisfies the threshold criterion ≥ th . A threshold of th = 1.2 nm was used in this work. The mean thickness ⟨ ⟩ of each particle (grey line) is obtained by averaging the height value within the particle boundary. The maximum thickness max (blue line) can also be obtained. (B) The Feret (caliper) diameter of a particle in the substrate plane, , is defined as the smallest distance between oriented parallel lines that encloses the particle. The value of depends on the orientation of the parallel lines relative to the particle. The Feret length (orange) and Feret width (pink) of the particle are defined as the maximum and minimum Feret diameter respectively. Note that the parallel lines that enclose and are not at perpendicular orientations (unlike the definition of the box length and box width , Supplementary Table 5). (C) Illustration of the effect of a tip artefact on a spherical nanoparticle (green) on a flat substrate. For a spherical nanoparticle, the bare particle diameter is accurately measured in the height profile but not in the lateral scan direction due to the width of the AFM tip tip , leading to an effective diameter eff being measured.
CNCs at a range of sonication doses were imaged and analysed using AFM (see Supplementary Methods section 12.9 and Supplementary Table 8    Remarkably, a power law relation between mean and max thickness ( max ∝ ⟨ ⟩ ) is well-described by an exponent = 1.32 ≈ 4/3 (red dotted line), rather than a linear fitting ( = 1, blue dotted line, shifted vertically for clarity). This scaling behaviour can be attributed to the bundled, fractal-like 3D morphology of the CNC particles. It should be noted that different particle populations (Aggregates, Bundles, Crystallites and Distorted crystallites) are expected to show different scaling behaviour, but the classification used for particle shapes from TEM images could not be directly applied to AFM shape data. AFM data can also be used to estimate the thickness of a given CNC from a TEM image by matching the particle length to a length-thickness calibration curve obtained from AFM image analysis. As shown in Supplementary Figure 14A, the AFM Feret length shows a clear positive correlation with mean thickness, which can be modelled by an empirical power law relation. Length values from AFM and TEM show fairly good agreement, even without correcting for the tip diameter (Supplementary Figure 14B). Consequently, the thickness of particles measured from TEM images was estimated by assuming TEM = AFM and applying the power law fitting from Supplementary Figure 14A. These thickness values were then used to estimate other shape properties (e.g. the 3D aspect ratio 3D ).

Estimation of ensemble size values from individual particle sizes
The size distributions obtained from TEM images can be used to estimate ensemble properties such as the mean particle cross-section from UV-vis transmission spectroscopy (Supplementary Methods, section 12.7, section 5) or the mean hydrodynamic diameter obtained from DLS measurements (Supplementary Methods, section 12.1). The mean particle cross-section was estimated using eq. (13) in section 5, while the hydrodynamic diameter was estimated by the method explained below. The mean hydrodynamic diameter ⟨ ℎ ⟩ obtained from a DLS measurement is the hydrodynamic diameter corresponding to the average translational diffusion coefficient ⟨ ⟩: where is the Boltzmann constant, is temperature, 0 is the suspension viscosity (assumed to be the viscosity of water). The average diffusion coefficient ⟨ ⟩ is weighted by the scattered light intensity, which scales with the particle volume squared. The particle sizes measured from TEM can be used to estimate the intensity-averaged diffusion coefficient: where is the particle volume and ∑ indicates summation of all the particles measured. The translation diffusion coefficient of CNCs can be estimated by assuming CNCs diffuse like ideal rods. The diffusion coefficient for an ideal rod of length and aspect ratio is (11): where ( ) is a correction added to account for end effects: To apply these equations to CNC suspensions, the particle length was assumed to be the box length ( = ) and the aspect ratio was assumed to be the 3D aspect ratio ( = 3D ). Note that these values do not take into account electroviscous effects due to the electric double layer around the particles in aqueous suspension. For the CNC suspensions used for DLS measurements in this work, the hydrodynamic diameter is ∼100 nm and the Debye length −1 ∼ 10 nm: in this limit ( ∼ 10), electroviscous effects are expected to be negligible (<5%), and are therefore not taken into account (12).
The estimated -average hydrodynamic diameter calculated using Equations (14) to (17) is shown in Supplementary Figure 15A alongside the experimental values from DLS. The particle cross-section was estimated using eq. (13) and is shown in Supplementary Figure 15B alongside values obtained from UV-vis transmission spectroscopy (Section 5). The estimated values capture the overall trends and show good agreement, especially at higher sonication doses. The discrepancies at low sonication dose can be attributed to the irregular shapes of large particles, which deviate from the cylinder model, and also the sensitivity of the scattering intensity to fluctuations in the number of large particles observed in TEM images. 10 Correlating CNC phase behaviour with particle morphology For cylindrical particles forming a lyotropic liquid crystal phase, the concentrations of the isotropic-biphasic and biphasic-anisotropic phase boundaries ( 0 and 1 respectively), and the position of the midpoint of the biphasic region ( = ( 0 + 1 )/2), are expected to be inversely proportional to the cylinder aspect ratio, as shown by Onsager and subsequent authors (13; 14). As shown in Supplementary Figure 16A, the biphasic midpoint is fairly well-described by a linear relation with inverse 3D aspect ratio (i.e. ∝ −1 3D ), in line with theoretical predictions. However, only 1 is observed to increase with sonication dose, while 0 appears to remain constant. In terms of re-scaled volume fraction 3D , only 1 3D significantly increases with sonication dose (Supplementary Figure 16B). This broadening can be attributed to an increase in the coefficient of variation (relative polydispersity) in 3D aspect ratiõ= √ (⟨ 2 ⟩ − ⟨ ⟩ 2 )/⟨ ⟩ 2 (note the 3D subscript has been omitted for clarity). Supplementary Figure 16C shows the variation iñwith re-scaled volume fraction, which shows trends similar to a previous theoretical study on length-polydisperse colloidal rods (15).

Classification of CNC particles
The classification of CNC particles into four classes (A, B, C, D) is based on their shape properties observed in TEM images, as described in the article. The relative number fraction of each particle class ( = , , , ) in the overall population is given by where is the number of particles in class . The relative number fraction for each sonication dose in shown in Supplementary Figure 17 Supplementary Figure 17: Relative number fraction  for each particle class = , , , .
Alternatively, the relative volume fraction of each particle class can also be calculated where is the total volume of all particles in class . To calculate , the volume of each CNC in class (index ) is estimated using the expression where is the projected area observed in the TEM image and ⟨ ⟩ is the estimated mean particle thickness (see section 8 for details). The total volume is then given by = ∑ ∈ (21) Note that the relative volume fractions are normalised such that ∑  = 1. The absolute volume fraction of particles of class (in the suspension) is given by =  CNC . The relative volume fractions versus sonication dose is shown in the article.
The differences in morphological properties between the sub-populations can be clearly seen in histograms for each population. Histograms for particle box length and 3D aspect ratio 3D of each class are shown in Supplementary Figure 18. Histograms for the cross-section aspect ratio expressed as XS,AE and XS,b (defined in Supplementary Table 6) are shown in Supplementary Figure 19. Histograms for the 2D isoperimetric quotient and estimated 3D isoperimetric quotient are shown in Supplementary Figure 20.
Supplementary Figure 18: Histograms for particle length and 3D aspect ratio 3D for each particle class.

Electrolytic conductivity and pH measurement
The conductivity and pH of CNC suspensions were determined using a platinum 2-pole conductivity probe (InLab 752-6MM, Mettler Toledo) or pH probe (InLab Micro Pro-ISM, Mettler Toledo) respectively. All measurements were performed at room temperature.

Optical spectroscopy of CNC photonic films
Left-circular polarised (LCP) reflectance spectra of CNC photonic films were obtained using the microscope setup used to collect polarised optical microscopy images (see Methods and Figure 1 of the main article). The light reflected from the sample passed through an LCP analyser, composed of an achromatic quarter-wave plate and linear polariser (Thorlabs WP25M-UB), before being transmitted to a UV-vis spectrometer (AvaSpec-HS2048, Avantes) via an optical fibre (600 µm core diameter, FC-UV600-2-SR, Avantes). Reflection spectra were normalised to a silver mirror (Thorlabs, PF10-03-P01).

Scanning electron microscopy (SEM) of CNC photonic films
Fully dry CNC films were pulled apart to expose their cross-sections. The films were then mounted onto steel stubs using conductive carbon tape. Samples were coated with platinum to a nominal thickness of 10 nm using a sputter coater (Quorum Q150T ES) to ensure good conduction of electrons. Micrographs were taken using a TESCAN MIRA3 FEG-SEM system using an acceleration voltage of 5 kV and a working distance of 3-6 mm.

Conductometric titration of CNC suspensions
In a typical titration procedure, 2.0 g of 2.0 wt% CNC suspension was added to 200 mL of 0.5 mM NaCl solution. The acidic CNC suspensions (with H + counter-ions on the CNC sulfate half-ester groups) underwent extensive dialysis against deionised water prior to measurement. An automatic titrator (Metrohm 856) was used to inject NaOH solution (10 mM) in 5 µL increments, while continuously recording the suspension conductivity. The surface charge per CNC dry mass (mmol/kg) was determined from the first equivalence point of the titration curve, obtained by a manual piecewise linear fitting.

Zeta potential of CNC suspensions
The CNC samples used for zeta potential measurements were identical to those used for DLS measurements (Supplementary Methods, section 12.1). The zeta potential was estimated from the measured electrophoretic mobility using the Smoluchowski limit of the Henry equation ( ≫ 1, ( ) = 1.5), which is the conventional choice for CNC suspensions (16). Measurements were performed in three batches of at least 50 runs each.

UV-vis transmission spectroscopy of CNC suspensions
UV-vis transmission spectra were obtained using a commercial spectrophotometer (Cary 4000). CNC samples were prepared at 0.1 wt% and measured in a quartz cuvette (Hellma 100-10-40) with 10 mm path length.

Cryogenic transmission electron microscopy (cryoTEM) of CNC suspensions
Cryogenic transmission electron microscopy (cryoTEM) imaging was carried out using a JEM 3200FSC field emission microscope (JEOL) operated at 300 kV in bright field mode with an Omega-type zero-loss energy filter. The images were acquired with a Ultrascan 4000 CCD camera (Gatan) and processed with Gatan Digital Micrograph software (version 1.83.842). Vitrified samples were prepared using EM GP2 Automatic Plunge Freezer by placing a 4-5 µL droplet of sample solution onto plasma-cleaned 300-mesh lacey carbon copper grids in a 90% humidity atmosphere, then blotted with filter paper for 0.5 -1.5 seconds, followed by immediate immersion into an ethane/propane mixture at −170°C. The samples were then cryo-transferred to the microscope, where their temperature was maintained at −187°C.

Atomic force microscopy (AFM) of CNC suspensions
Atomic force microscopy (AFM) images of the cellulose nanocrystals were acquired at ambient conditions using a scanning probe microscope (Agilent 5500 SPM) in tapping mode with an AFM probe (OTESPA-R3). A square of mica (2 cm 2 ) was freshly cleaved to obtain a mirror smooth surface. A droplet (100 µL, 0.1 wt%) of poly-L-lysine (P8920, Sigma, M W = 150-300 kDa) was deposited for 1 minute, after which it was rinsed off with deionised water and dried under nitrogen gas flow. Then, the CNC sample (150 µL, 0.001 wt%, pH = 3) was deposited and incubated for 3 minutes after which it was washed off with deionised water and dried under nitrogen gas flow. Finally, the sample was dried in the oven for 30 minutes at 50°C and then kept at ambient conditions in a closed dish before the measurements. Scans were typically performed over a 4x4 µm 2 area with 2048 points per line at 0.6 Hz to acquire the final images with ∼2 nm resolution.
CNC particle height statistics were extracted from AFM images using Gwyddion software (17). The images were processed in six steps: (1) removing the background height variation using a fifth-order polynomial fitting (2) aligning rows by median values (3) healing scars (4) flattening the base (5) setting the zero offset to the median image height and finally (6) Gaussian filtering with 2 pixel resolution.
To estimate the AFM tip diameter, AFM images were also obtained for spherical gold nanoparticles with diameter ≈ 15 nm. The tip diameter was estimated by the difference between the max height of the particle and the apparent lateral diameter (Supplementary Figure 11C). Measurement on 38 particles gave tip = 14.2 ± 1.1 nm (Supplementary Figure 21) Histogram of estimated tip diameter tip = eff − for spherical gold nanoparticles.

Transmission electron microscopy (TEM) shape analysis
As previous authors have noted, there is great variability in CNC size data obtained from TEM images, even for two users manually measuring identical experimental data (18). The tracing method used in this work is therefore described in detail below to aid comparison with other works.
CNC particles as observed in TEM images were manually traced to extract size and shape properties. Tracing was performed on a touch-screen device using a stylus and the "Freehand Selections" tool in Fiji/imageJ. In negatively-stained TEM images, CNCs generally appear as bright spindle-shaped objects surrounded by a dark "halo" or outline created by the accumulation of staining agent around the particle. The CNC particle was taken to be the entire bright area within this dark outline. The particle areas were filled white on the original image and then selected by thresholding the image.
We found that suspending the CNCs in an aqueous pH 3 solution of sulphuric acid dramatically reduced the occurrence of artefacts due to particle aggregation on the dried TEM grid, in agreement with previous work (19). Therefore, any single continuous bright region, regardless of shape, was assumed to be a single CNC particle. In particular, even if the shape could be interpreted as two elongated particles overlapping, the shape was still assumed to be a single particle.
The traced shapes were analysed using the ImageJ Shape Filter plugin, filtering for all particles larger than 70 nm 2 to eliminate any artefacts due to pixel noise. The data were exported in .csv format and further processed using a custom Python script.